Simulation based on Transient Stability Analysis of Synchronous
Generator In Power System Using Direct Method
Mr.Parth J.Pandya 1|Prof. Ramji V.Kanani2 |Prof. Ajit J.Pujara3
1 M.Tech,Student, Electrical Engineering Department, 2 Assistant Professor, Electrical Engineering Department,
Swarrnim Institute of Technology Gandhinagar Swarrnim Institute of Technology Gandhinagar
Swarrnim Startup and Innovation University Swarrnim Startup and Innovation University
Email: - [email protected] Email:- [email protected]
3H.O.D, Electrical Engineering Department,
Swarrnim Institute of Technology Gandhinagar
Swarrnim Startup and Innovation University
Email: - [email protected]
ABSTRACT
Transient stability of synchronous generator can be analysed by different methods like time domain
method, direct method, approximation method and artificial intelligent method. Transient stability analysis of multi
machine system is analysed using time domain method, direct method and approximation method.
Time domain method, direct method and approximation method are compared in this report
using Critical Clearing Time (CCT). Time domain method is most accurate method and slowest method. Direct
method is less accurate than time domain method but more accurate than approximation method. Approximation
method is least accurate but fastest method than other methods. In approximation method, mathematical
formulation is done in this report which can be used in parametric analysis. The simulation is performed using
MATLAB/ Simulink software.
Keywords: Transient stability, time domain method, MATLAB/ Simulink software.
I.INTRODUCTION
I.I Introduction of Transient Stability
Electricity is the backbone of human life that is why power system should be reliable, stable and
qualitative.Power system stability can be defined as the ability of a power system to remain in a synchronism in a
normal operating condition and after the occurrence of disturbance in the system [1][2].
During normal operating conditions of the power systems (in steady state), two main conditions should be satisfied
for generators: (1) Rotors should be in synchronism. (2) Frequency of all generated voltages should be equal [4].
These conditions are violated when any type of disturbances are developed on the power system. Due to these
disturbances instability in power system is developed. These disturbances may be small or large. Power system
must be able to withstand against these disturbances.
The ability of a power system to remain in synchronism is called rotor angle stability [2]. The ability of the power
system to maintain synchronism due to small disturbances is known as small signal stability [2]. The ability of the
power system to maintain synchronism due to large disturbances is known as transient stability [2]. Transient
stability analysis of synchronous generator can be done using different methods. Power system stability can be
classified as shown in figure 1.1
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Figure-1.1 Types of power system stability phenomena Adapted from [Kundur and Morisson, 1997a]
I.II Concept of Transient Stability
Prime mover is used to drive the rotor of synchronous generator. So that frequency of the terminal voltage
of the generator depends on the speed of rotor. Rotor mechanical speed is synchronized with the frequency of the
stator electrical quantities. When two or more synchronous generators are connected, stator voltage and current of
each generator must have the same frequency. The rotors of all interconnected synchronous generators must be in
synchronism. During normal operating conditions of power system, Mechanical input power (Pm) from prime
mover to generator shaft and generated electrical power (Pe) should be in balanced condition.
When large disturbances (like a fault on the network, failure of equipments, sudden change in load, and loss
of a line or generator) are developed on power system, the maintenance of stability of rotor angle is known as
transient stability. Due to these disturbances the synchronous machines may loss synchronism
For stability, the system oscillations must be damped, therefore the inherent forces in the system start to
reduce oscillations.
I.III Swing Equation
The swing equation shows the electromechanical oscillations or dynamics in a power system. This equation
provides the relative motion or acceleration.
Figure-1.2 Generator-turbine torque balance
Synchronous generator is considered with torque e and running with synchronous speed.
During steady state condition, mechanical torque, em
A disturbance occurred will result in accelerating/decelerating torque.
As per torque law,
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(1)
If mechanical speed is multiplied both side,
(2)
Swing equation in terms of inertial constant M
(3)
If damping is considered then,
(6)
If equation is converted into per unit values,
(7)
Electrical active power,
(8)
(9)
From (1) and (2),
(10)
Where, δ is the power angle
ω = Angular velocity(rad/s)
J = Moment of inertia (kg.m2)
M = ω.J
H = Inertia constant
D = Damping coefficient
I.IV Factors Affecting Transient Stability
Generator loading
Fault type and location (network detail)
Fault clearing time
Generator parameter (reactance, inertia etc.)
Excitation of generator
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Infinite bus voltage magnitude
Figure-1.3 shows the characteristic of a synchronous generator which shows the stable and unstable
condition. In Case-1, the rotor angle first start to increases and become maximum, then starts to decrease and
oscillates with reduced magnitude. This is a transient stable condition. In Case-2, the rotor angle increases and
goes to infinite. This is the instability of first swing. In Case-3, for first swing the system is stable but at last due to
increasing magnitude system becomes unstable. When the post fault steady state condition is small signal unstable
then this form of instability occurs.
Figure-1.3 Rotor angle response to transient disturbance
In transient stability analysis, variation of rotor angle and speed of rotor of synchronous generator can be
determined that shows the relation with time and explains about the stability of the system.
II. Methods of Transient Stability Analysis
Transient stability of synchronous generator in power system can be analysed by swing equation which is
a nonlinear differential algebraic equation. In order to solve these equation or to analyse stability, different type of
methods are used which are mentioned below
Time domain method
Direct method
Equal area criteria method
Energy based Lyapunov’s method
o Closest UEP Method
o Controlled UEP Method
o BCU Method
o PEBS Method
Approximate Method
Artificial intelligent method
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III. Problem Formulation
Transient stability analysis can be done using different methods. Aim of all methods is to
determine Critical Clearing Time (CCT).
III.I Objective:
Comparison of “Critical Clearing Time” of different methods of transient stability analysis of
synchronous generator in power system is the main objective of this work.
Methods for comparison:
1. Time Domain Method
2. Direct Method
3. Approximation Method
III.II Considered system In this System, 2 machines, 9 buses (one bus as infinite bus) are considered [3], [9]. For transient stability
analysis, in this system, three lines to ground fault is considered near 7th bus, and on 5-7 line. After fault clearing,
5-7 line is removed from the system. In this given system, two synchronous generators are connected; one is
connected on 1st bus and second is connected on 2nd bus. All parameters of the considered system are shown in
below figure. Three loads are connected on the system; load A is connected on 5thbus, load B is connected on 6th
bus and load C is connected on 8th bus. Bus number 3 is considered as a infinite bus.
Table 3.1 Generator Data
Generator Data
Generator 1 2
Rated MVA 192 128
kV 18 13.8
Power factor 0.85 0.85
Type steam Steam
Speed 3600 r/min 3600 r/min
dx 0.8958 1.3125
'
dx 0.1198 0.1813
qx 0.8645 1.2578
'
qx 0.1969 0.25
)(leakagelx 0.0521 0.0742
'
0d 6 5.89
'
0q 0.535 0.6
Stored energy at rated speed 640 MW.s 301 MW.s
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Figure-3.1 Considered system for transient stability analysis
Reactance values are in pu on a 100 MVA base.
Load A: 1.25(0.5), Load B: 0.9(0.3), Load C: 1(0.35), where P(Q) format is taken
Equivalent shunt admittance, for load are given as below,
Load-A: yL5= 1.261 – j0.5044
Load-2: yL6= 0.8777 – j0.2926
Load-3: yL8= 0.969- j0.3391
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IV.I Transient stability analysis methods
Figure- IV .1 Transient Stability Analysis Methods
V. Simulation and result
V.I Time domain method
During transient analysis of power system, numbers of dynamic equations are there for speed and
acceleration of synchronous generators. These equations are also known as swing equations. These equations are
non linear differential equations. To solve these equations numerical integrations techniques are used.The time
domain numerical integration technique is not suitable for on line security analysis due to the long run timesfor
simulation. In numerical integration method step size of time is used. This run time depend on step size. If step
size is large then run time is small but accuracy is less. Different numerical integration methods are
Euler method
Trapezoidal rule
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Runge kutta method
Point by point method
At present, stability analysis programs are based on step by step numerical integrations
technique.
Modelling of components is required in time domain method.
Modelling components:
Synchronous generator modelling
Excitation system modelling
Transformer and transmission line modelling
Different types of load modelling
Facts controller modelling
Turbine and speed control scheme modelling
As per 1986 IEEE task force report, Different types of models are possible in case of
synchronous generator that are given as below,[16]
Model 0.0 (Classical model)
Model 1.0 (Only field circuit)
Model 1.1 (One field circuit on d-axis and one damper circuit on q-axis)
Model 2.1 (One field and one damper circuit on q axis, one damper on d axis)
Model 2.2 (Two circuit on d-axis and two circuit on q-axis)
Model 3.2 (Three circuit on d-axis and two circuit on q-axis)
Model 3.3 (Three circuit on d-axis and three circuit on q-axis)
Mostly 1.1 and 2.1 model is used in practice as detail model.
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V.II Synchronous generator modelling (2.1 model) [13]
Figure-5.1 Synchronous generator stator rotor circuits
Steps for modelling:
Forming mathematical equations from circuit in abc form.
Park’s transformation is used to change time variant quantities into time invariant
quantities.
Forming mathematical equations in dq0 form.
Equations in abc parameter from circuits,
(11)
(12)
Here,
Relation between flux and current,
(13)
Inductance matrix in abc parameter,
(14)
Park’s transformation,
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Where,
Voltage equations in dq0 form after applying park’s transformation,
(15)
(16)
(17)
(18)
(19)
(20)
Flux equations in dq0 form after applying park’s transformation,
(21)
(22)
(23)
(24)
(25)
Using above mathematical equations, MATLAB model can be prepared which can be used in
time domain for transient stability analysis.
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V.III 2.1 Model in MATLAB
(a)
(b)
Field Circuit Model
(c)
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Damper Circuit Model
(d)
Armature Circuit Model
Figure-5.2 Synchronous generator 2.1 model in MATLAB including (a),(b),(c) and (d)
V.III Time Domain Method
Two machines, nine buses system is considered. In transient stability analysis classical
model of synchronous machine is used. To determine classical model, initial power flow of
system is required that is why PSAT tool box is used as shown in figure.
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Figure-5.4 System in PSAT tool box
Power flow Result
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MATLAB Model
Figure-5.4 System MATLAB model
Figure-5.4 System subsystem-1 MATLAB model
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Figure-5.4 System subsystem-2 MATLAB model
Results for Fault Clearing Time = 0.1 second
Figure-5.5 Results for fault clearing time 0.1 second
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Results for Fault Clearing Time = 0.11 second
Figure-5.6 Results for fault clearing time 0.11 second
-2
0
2
4
-2
0
2
4
-2
0
2
4
6
8
Delta-1
Critical Energy (Ec)
Delta-2
Critica
l Ener
gy (Ec
)
Figure- Critical Energy (Ec)
Formula of critical energy (Ec) with respect to SEP is given as equation. Using this equation, MATLAB
coding is prepared as given in Appendix-A.
Result of critical energy (Ec) is shown in figure in which energy variation is shown with respect to both generator
rotor angles.
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Figure- Energy Level
Critical energy can be obtain by contour graph as shown in figure-5.8, in which critical energy is
given by Ec= 1.0525
Total energy of fault on condition can be determined using equation. MATLAB coding
for total energy of fault on system is given in Appendix-A.
Fault on system is dynamic system, energy of this system increases due to fault occurred. Here total
energy and critical energy are compared. Result can be obtained as shown in below figure.
From figure, it can be said that Critical Clearing Time (CCT) is 0.099 second.
From figure-, CCT, tD= 0.099 second
From figure-, CCT, tT= 0.1 second
VI. Conclusion
Time domain method is most accurate method among other methods, and it is
slowest method than other methods.
Direct method is less accurate method than time domain method but particularly
in this case its accuracy almost same as time domain method. This method is
faster than time domain method.
Approximation method is least accurate method and fastest than other methods.
VII.REFERENCES
[1] IEEE/CIGRE Joint Task Force on Stability Terms and Definitions, “Definition and
classification of power system stability,” IEEE Trans. Power Syst., vol. 19, no. 2, pp.
1387– 1401, May 2004.
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[2] P. Kundur, “Power System Stability and Control” New York: McGraw-Hill, 1994
[3] P. M. Anderson and A. A. Fouad, “Power System Control and Stability” 2nd ed.
Piscataway, NJ, USA: IEEE Press 2003.
[4] SinaYamacCaliskan and Paulo Tabuada, “Compositional Transient Stability Analysisof
Multimachine Power Networks”, IEEE transactions on control of network systems, vol. 1,
no. 1, march 2014
[5] M. Pavella, D. Ernst, and D. Ruiz-Vega, “Transient stability of powersystems: A unified
approach to assessment and control,” in Kluwer’s Power Electronics and Power Systems
Series, Kluwer Academic Publishers, 2000.
[6] Hsiao-Dong Chang And Chia-Chi Chu, “Direct Stability Analysis of Electric Power
Systems Using Energy Functions: Theory, Applications, and Perspective”, Proceedings of
the IEEE, vol. 83, no. 11, November 1995
[7] Thanh Long Vu and Konstantin Turitsyn, “Lyapunov Functions Family Approach to
Transient Stability Assessment”, IEEE transactions on power systems,vol. no.1 february
2015
[8] A. A. Fouad and V. Vittal, Power System Transient Stability Analysis: Using the Transient
Energy Function Method. NJ: Prentice-Hall: Englewood Cliffs, 1991.
[9] Lewis G. W. Roberts, Alan R. Champneys, Keith R. W. Bell, and Mario di
Bernardo,“Analytical Approximations of Critical ClearingTime for Parametric Analysis
of PowerSystem Transient Stability”, IEEE journal on emerging and selected topics in
circuits and systems, vol. 5, no. 3, September 2015
[10] Marian Anghel, Federico Milano and AntonisPapachristodoulou, “Algorithmic
Construction of Lyapunov Functions for Power System Stability Analysis”, IEEE
transactions on circuits and systems, January 14, 2013
[11] M. A. Pai and Peter W. Sauer, “Stability Analysis of Power Systems by Lyapunov's Direct
Method”, IEEE control systems magazine, January 1989
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